Question

A (2, 3), B (-1, 1) are two points if P is a point such that ZAPB =90° then the locus of p is​

Answer 1

Answer:

x^2+y^2-x-4y+1=0

Step-by-step explanation:

Given,

points are A(2,3),B(-1,1)

Let, P(x,y) be a point in locus then from given condition.

<APB=90°

triangle APB is a right angled triangle.

so,AB^2=AP^2+BP^2

(x-2)^2+(y-3)^2+(x+1)^2+(y-1)^2=(2+1)^2+(3-1)^2

x^2+y^2-4x-6y+13+x^2+y^2+2x-2y+2=13

2x^2+2y^2-2x-8y+2=0

2(x^2+y^2-x-4y+1)=0

Hence, the equation of locus of a point P(x, y) is x^2+y^2-x-4y+1=0